In coherent digital optical receivers, blind carrier phase recovery may incur errors, causing phase slips. A channel including blind phase estimation is modeled as an additive white Gaussian noise (AWGN) channel, affected by random phase slips that occur with a certain probability. For such a channel, block differential modulation (BDM) has been recently shown to achieve almost the same capacity as coherent AWGN channels. This paper proposes a concatenated coding scheme, with an inner code based on low-density parity-check (LDPC) codes, that embeds block differential demodulation, to make it robust to occasional phase slips. This additional feature comes at no practical cost and performs very close to a standard soft decoded LDPC code. The first design is a binary LDPC code, robust to phase rotations at multiples of $pi$, to be used with BPSK. Then, the concept is extended to quaternary LDPC codes, robust to phase rotations at multiples of $pi /2$, that can be used with 2-D digital constellations such as QPSK and 16-QAM.